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Xiudi Tang

Visiting Assistant Professor

Xiudi Tang

Educational Background

Ph.D. (2018) University of California, San Diego

Website(s)

Departments/Programs

  • Mathematics

Research

Differential Geometry, Symplectic Geometry, Integrable Systems

I study the symplectic structures on noncompact manifolds, and on integrable systems with singularities. Currently, the following questions have been addressed: Which volume forms defined fiberwise on a fiber bundle are equivalent? Which symplectic forms on a noncompact manifold are equivalent? Which integrable systems are equivalent near a singular fiber? I answered the last question by a classification which I would like to find connections with moduli spaces of integrable systems, quantum integrable systems, and the mirror symmetry.

Publications

  • Symplectic stability on manifolds with cylindrical ends (with Sean Curry and Álvaro Pelayo), The Journal of Geometric Analysis 28 (2018).
  • Moser-Greene-Shiohama stability for exhausted bundles (with Álvaro Pelayo), arXiv:1607.03800 (2018).
  • Moser-Greene-Shiohama stability for families (with Álvaro Pelayo), Journal of Symplectic Geometry, to appear.
  • Vũ Ngọc's Conjecture on focus-focus singularities with multiple pinched points (with Álvaro Pelayo), arXiv:1803.00998 (2018).